Share Email Print

Proceedings Paper

Unification, H-duality, and data truncation in image reconstruction from divergent beam projections
Author(s): Guang-Hong Chen
Format Member Price Non-Member Price
PDF $14.40 $18.00
cover GOOD NEWS! Your organization subscribes to the SPIE Digital Library. You may be able to download this paper for free. Check Access

Paper Abstract

In this paper, a unified framework of image reconstruction from both fan-beam and cone-beam projections is formulated by using intermediate functions. The intermediate function has an imaginary part and a real part. The causality principle is used to prove that the imaginary and real part is mutually linked by a Hilbert transform. Using this link, it is shown that image can be reconstructed by using either the real part or the imaginary part of the intermediate function. Thus there exist two fundamental image reconstruction schemes in image reconstruction from divergent beam projections. One scheme only uses the imaginary part of the intermediate function, while the other scheme only uses the real part. Two schemes are dual to each other by Hilbert transform in intermediate functions. Thus this dual nature is called H-duality. One of the paired dual formulas explicitly allows data truncation, while the other one does not. However, they are equivalent in the sense that both of them are mathematically exact image reconstruction formulas provided the measured data is sufficient for both formulas and is free from noise. Practically, a fan-beam image reconstruction formula is identified to solve the fan-beam data truncation problem.

Paper Details

Date Published: 26 October 2004
PDF: 12 pages
Proc. SPIE 5535, Developments in X-Ray Tomography IV, (26 October 2004); doi: 10.1117/12.560178
Show Author Affiliations
Guang-Hong Chen, Univ. of Wisconsin/Madison (United States)

Published in SPIE Proceedings Vol. 5535:
Developments in X-Ray Tomography IV
Ulrich Bonse, Editor(s)

© SPIE. Terms of Use
Back to Top